Palmero Matheus S, Caldas Iberê L, Sokolov Igor M
Instituto de Física, Universidade de São Paulo, São Paulo, SP, Brazil.
Institut für Physik, Humboldt-Universität zu Berlin, Berlin, Germany.
Chaos. 2022 Nov;32(11):113144. doi: 10.1063/5.0102424.
In this work, we show that a finite-time recurrence analysis of different chaotic trajectories in two-dimensional non-linear Hamiltonian systems provides useful prior knowledge of their dynamical behavior. By defining an ensemble of initial conditions, evolving them until a given maximum iteration time, and computing the recurrence rate of each orbit, it is possible to find particular trajectories that widely differ from the average behavior. We show that orbits with high recurrence rates are the ones that experience stickiness, being dynamically trapped in specific regions of the phase space. We analyze three different non-linear maps and present our numerical observations considering particular features in each of them. We propose the described approach as a method to visually illustrate and characterize regions in phase space with distinct dynamical behaviors.
在这项工作中，我们表明，对二维非线性哈密顿系统中不同混沌轨迹进行有限时间递归分析，可为其动力学行为提供有用的先验知识。通过定义一组初始条件，将它们演化到给定的最大迭代时间，并计算每个轨道的递归率，可以找到与平均行为有很大差异的特定轨迹。我们表明，具有高递归率的轨道是那些经历粘性的轨道，它们被动态地限制在相空间的特定区域。我们分析了三种不同的非线性映射，并根据它们各自的特定特征给出了数值观测结果。我们提出将所描述的方法作为一种直观展示和刻画相空间中具有不同动力学行为区域的方法。
